The living wage has been uprated by the Joseph Rowntree Foundation. The least a family needs for decent survival has been lifted to £7.45 an hour, £8.55 in London. Both Miliband brothers have put Labour as leaders of the cause. Labour councils and Labour cities from Glasgow and Newcastle to Cardiff and Leeds have adopted it for their staff and contractors.

Boris Johnson has kept Ken Livingstone's commitment to it for the GLA. David Cameron supported it before the election, to make "fairness hard-wired into pay scales up and down the country", but he dropped it once in power, not even paying it to Whitehall cleaners. Downing Street now says it might "reduce business flexibility". The Lib Dems said that instead of "burdening" employers with a living wage, they had helped the low-paid by cutting tax, yet they know their personal allowance increase gives zero to the lowest third, and most to the top third. However, the groundswell for a living wage may yet force the hand of all parties.

This has been a long time brewing. Objectors at first said it was impossible: it would cause catastrophic job loss. But for 10 years Citizens UK kept plugging away, patiently wearing down resistance and steadily arm-twisting more employers, most of whom could easily afford it. Summoning faith groups to work with trade unions, it confronted employers in ways that confused them – not with industrial threats but with shame. Once, unable to get a meeting with a key CEO, Citizens UK asked the local vicar to knock on the man's door to talk about paying his staff better. The CEO was so unnerved, he succumbed.

Living wage employers now include Barclays, HSBC and KPMG. But these can make the gesture at little cost, with just a handful of low-paid staff. Although so far only 45,000 workers have benefited, a great tipping point may be close. InterContinental Hotels Group, the company behind Holiday Inn, has agreed to back the London living wage – that's the first employer with large numbers of low-paid chambermaids. One of the biggest supermarkets is on the verge of paying the living wage to all its checkout staff: that might tip the whole sector. John Lewis still hovers uncertainly: its outsourced low-paid cleaners are not partners. On 17 November its stores will be picketed by Citizens UK, trying to persuade partners at the counters to vote to take agency cleaners into this most famous mutual.

Ed Miliband, speaking in Islington, celebrated the tide of Labour councils signing up. Islington's ground maintenance contract, worth £20m, employs 80 people, all now to get the living wage, with the company absorbing the whole cost. His living wage would be voluntary, but he would make companies publish not just top salaries, but their low pay numbers too, exposing those paying wages no family can live on. The IFS says the Treasury gains £1,000 in tax and saved credits for each living wage worker. Why should the taxpayer subsidise Scrooge employers?

But a living wage is only part of the cure for Britain's dangerous epidemic of inequality. Pay was at its most equal in the late 1970s, when history went into sudden reverse. Top pay soared while middle to bottom rates fell. The ONS found the share of national income going to wages shrank, while the share going to profits grew. Middle incomes have stagnated for the last decade: ahead the trajectory is ever-accelerating inequality.

The IFS says that if the 7-8 million low-paid moved to a living wage, that would significantly reduce earnings inequality. But here's the catch: it would have much less impact on actual incomes. As people earn more, most lose 70% of the gain in reduced tax credits. For dignity, to move pay forward, the living wage is essential – but it's not enough. For households to earn more, mothers need to be able to work. That's why the Resolution Foundation, Progress and the IPPR all press Labour to offer universal virtually free childcare and social care. All that is relatively easy and popular. But there has been a great yawning silence from Labour on the more politically difficult subject of galloping inequality. Labour mumbles on benefits, afraid of public hostility.

On the Andrew Marr Show this week Duncan Smith repeated his untruths about mythical families workless for two and three generations, from the great Tory demonology of scroungers. He knows well they barely exist: research shows double-generation worklessness is very rare, and no one has yet found real-life examples of three generations who never worked: bottom rung workers are mainly in and out of temporary, insecure work.

Where is Labour's defence of jobless strivers? Where is its forensic debunking of benefit myths? Where is its outrage at the idea that the third child of sick or unemployed families should be cut off? Benefit cuts are popular for lack of Labour defending the already poor from cuts that send them into food-bank destitution. Labour is good on the living wage, but now let's hear more indignation at this wicked pauperisation.